Commentary on ‘Thermodynamic analysis of the permeability of biological membranes to non-electrolytes’ by O. Kedem and A. Katchalsky Biochim. Biophys. Acta 27 (1958) 229–246

Malignant cells can be ablated by a specific treatment temperature during magnetic hyperthermia, which is induced by the power dissipation of magnetic nanoparticles (MNPs) inside tumor region under an alternating magnetic field. MNPs contained in nanofluid need to be transferred to tumor region before therapy can begin, and one of the most prominent methods is direct injection. Although different aspects of this area are covered in literature, the study of models which consider the combined effects of nanofluid transport and heat generation on the ablation of malignant cells still lacks enough attention. A complete computational model is developed in this paper to evaluate the survival rate of malignant cells for a proposed geometric model when intratumoral injection of MNPs is considered. The mathematical model incorporates the transport of nanofluid inside the bio-tissue, the heat generation of MNPs during ablation, the heat transfer of bio-tissue, and the cell death probability based on the Arrhenius model. The concentration distribution of nanofluid and the treatment temperature profile inside bio-tissue are obtained by considering the finite element method with the proposed boundary and initial conditions. Simulation results demonstrate that the death rate of malignant cells can be considerably improved when a proper critical power dissipation of MNPs is designed and enough diffusion duration is considered for therapy. With further developments, the model may be used for the planning of magnetic hyperthermia.